During transmission of an information signal from a transmitter to a receiver, either the frequency or the amplitude of the information signal is typically modulated. When the amplitude of the information signal is modulated, the signal is able to transmit a substantial amount of information in a relatively short bandwidth. A carrier frequency at which an amplitude modulated information signal is transmitted is generally several hundred kilohertz, while an information bandwidth may be only ten to twenty kilohertz. Similarly, when a carrier frequency is modulated by an information signal, the information is transferred at a frequency in the megahertz range.
Most receivers, however, operate at significantly lower frequencies than the transmission frequency of either amplitude or frequency modulated signals. For example, an analog to digital converter is necessary to convert a transmitted analog signal to a digital signal for subsequent manipulation by the receiver. However, the operating frequency of an analog to digital converter is typically less than one hundred kilohertz. Therefore, the transmission frequency of either an amplitude modulated signal or a frequency modulated signal must be down converted until a frequency is reached at which the analog to digital converter may function properly. Additionally, the frequency of the digital signal, the sampling frequency, provided by the analog to digital converter must be at least two times a highest frequency component of the transmitted information signal according to the Nyquist Criteria.
To achieve these requirements, the frequency at which the modulated signal is provided to the receiver is typically multiplied by a reference clock signal. When multiplying two frequencies which are either sine or cosine waves, the product of the "multiply" operation creates two components. A first component is simply the difference between the two frequencies, and a second component is the addition of the same two frequencies. The multiplied modulated information signal may then be provided to an oversampling analog to digital (A/D) converter at a frequency which will allow the A/D converter to function efficiently. A sampling clock provides a signal to the A/D converter such that the modulated information is converted to a digital form and output at a predetermined sampling frequency. The predetermined sampling frequency is typically a fraction of an input clock frequency input to the A/D converter and is dependent on the specifications of the A/D converter. For example, in a commercially available sigma-delta A/D converter sold by Motorola Inc. as the DSP56ADC16, the input clock frequency is one hundred twenty-eight times the sampling frequency of an output signal of the A/D converter.
Although the receivers described above provide a modulated signal at a lower frequency, additional phase error is introduced by the differing phases of the reference clock signal and the sampling clock. The additional phase error is then reflected in the digital information signal output from the A/D converter.
Additionally, the signal provided by the A/D converter must be demodulated by the receiver circuitry. A demodulation operation is dependent on the ratio of the center frequency of the signal input to the A/D converter and the frequency of the signal output provided by the A/D converter. Typically, either the cosine or sineof the ratio must be calculated for subsequent use in the receiver. To calculate either the cosine or sine of a value, the receiver must provide a memory storage table from which the cosine or sine value may be interpolated. Interpolation between table values often requires intensive instructions and a significant amount of time. Therefore, both the phase error and the form of a modulated signal do not allow the signal to be readily demodulated in a timely manner.